{
 "metadata": {
  "name": "",
  "signature": "sha256:877e67f888b20d7d68aaa38d017ccdfb1f6c49d8c1d3b7b4760f3f253423809a"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "# Introduction to design matrices\n",
      "\n",
      "[Tom Wallis](http://www.tomwallis.info) and [Philipp Berens](http://philippberens.wordpress.com/)\n",
      "\n",
      "\n",
      "The University of T\u00fcbingen\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# import necessary modules:\n",
      "import numpy as np\n",
      "import pandas as pd\n",
      "import patsy\n",
      "import seaborn as sns\n",
      "import statsmodels.api as sm\n",
      "import statsmodels.formula.api as smf\n",
      "import statsmodels.stats as sm_stats\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "%matplotlib inline\n",
      "\n",
      "sns.set_style(\"white\")"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "skip"
      }
     },
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "# Introduction\n",
      "\n",
      "The Generalised Linear Model (GLM) is a flexible way to combine different *predictor variables* to predict the value of a *response variable*. Many common statistical procedures are types of GLMs - t-tests, multiple regression, ANOVA, ANCOVA, etc. Furthermore, many more complicated statistical procedures are extensions of GLMs. An understanding of how GLMs work is therefore very useful."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "In the next few lectures we want to provide an overview of how GLMs work, with some simple examples. In particular, we want you to understand\n",
      "  + how to build design matrices\n",
      "  + the meaning of coefficients in a design matrix\n",
      "  + what a link function is\n",
      "      \n",
      "      \n",
      "      \n",
      "      \n",
      "      "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "# General form of the model\n",
      "\n",
      "The general form of a GLM can be written as \n",
      "\n",
      "$y = f(\\mathbf{X}\\beta) + \\epsilon$\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "- $\\mathbf{X}$: the design matrix, where columns are predictors, rows are observations\n",
      "\n",
      "- $y$ is the response variable we're trying to predict (a column vector)\n",
      "\n",
      "- $\\beta$ is a vector of weights, with the same length as the number of columns in the design matrix\n",
      "\n",
      "- $\\mathbf{X} \\beta$ is called the *linear predictor*\n",
      "\n",
      "- $f()$ is some transformation of the weighted design matrix (the link function). Examples include logistic, logarithmic, Poisson...\n",
      "\n",
      "- $\\epsilon$ is random noise of some type."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<img src=\"pics_for_lectures/pics_for_lectures.001.png\">"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "(note that in the picture above, the vector of weights $\\beta$ should really appear tall rather than wide because it's a column vector; I've drawn it this way to emphasise that it has the same *length* as the number of *columns* in $\\mathbf{X}$)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "Another way to write $\\mathbf{X}\\beta$ is in vector notation:\n",
      "\n",
      "$x_1\\beta_1 + x_2\\beta_2 + ... + x_n\\beta_n$\n",
      "\n",
      "- $x_n$ are column vectors\n",
      "- $\\beta_n$ is a scalar\n",
      "\n",
      "So the term $\\mathbf{X}\\beta$ is a linear weighted sum of predictors (i.e., it's a *linear* model). Let's look at a concrete example of this in action."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "# Example: simple linear regression\n",
      "\n",
      "Let's go back to our \"Sleep in Mammals\" dataset from the dataframe / plotting lecture.\n",
      "\n",
      "First, we import the data, drop missing cases, and create our log bodyweight variable."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# import the dataset csv file into a Pandas dataframe object:\n",
      "sleep = pd.read_csv('../Datasets/sleep.txt', sep='\\t') \n",
      "sleep = sleep.dropna(axis=0)  # drop on axis 0 (i.e. rows)\n",
      "sleep['log_BodyWt'] = np.log(sleep['BodyWt'])\n",
      "sleep.info()"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "<class 'pandas.core.frame.DataFrame'>\n",
        "Int64Index: 42 entries, 1 to 60\n",
        "Data columns (total 12 columns):\n",
        "Species        42 non-null object\n",
        "BodyWt         42 non-null float64\n",
        "BrainWt        42 non-null float64\n",
        "NonDreaming    42 non-null float64\n",
        "Dreaming       42 non-null float64\n",
        "TotalSleep     42 non-null float64\n",
        "LifeSpan       42 non-null float64\n",
        "Gestation      42 non-null float64\n",
        "Predation      42 non-null int64\n",
        "Exposure       42 non-null int64\n",
        "Danger         42 non-null int64\n",
        "log_BodyWt     42 non-null float64\n",
        "dtypes: float64(8), int64(3), object(1)\n",
        "memory usage: 4.3+ KB\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "g = sns.jointplot(\"log_BodyWt\", \"TotalSleep\", sleep)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {
        "png": {
         "height": 426,
         "width": 423
        }
       },
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAA04AAANUCAYAAACE7X18AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJEmSahicJEmSJKnG/weI88VJeCvZxwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10561eef0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see that the log of bodyweight seems to be related to TotalSleep approximately linearly (although the variance is higher for low bodyweights).\n",
      "\n",
      "**How many hours does a species of animal sleep on average, given its bodyweight?**\n",
      "\n",
      "To answer this question we can use a linear regression. We have a single *predictor* variable (the log of bodyweight) to predict our *response variable* of interest (Total hours of sleep). \n",
      "\n",
      "As you know from high school maths, the equation for a line can be written as $y = mx + c$. That is, we would like to estimate two parameters: the a slope as a function of $x$, and an intercept (the value of $y$ when $x$ is zero). "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Design matrices\n",
      "\n",
      "The design matrix $\\mathbf X$ has *predictor variables* in its columns. Remember that we will estimate one parameter (the $\\beta$ weight) for *each column of the design matrix*. \n",
      "\n",
      "The design matrix is not necessarily just a copy of the columns in our data frame. Sometimes variables need to be transformed to have a certain meaning within the model. We can use a module called *Patsy* to create design matrices automatically from our specification of the model.\n",
      "\n",
      "## Patsy and *S*-style formulae\n",
      "\n",
      "The Patsy package allows us to specify the model we want to fit in a high-level formula language, based on the one used in the ancient *S* statistical language (and now more recently in *R*). \n",
      "\n",
      "Patsy allows us to specify\n",
      "\n",
      "- our model\n",
      "- the data frame containing the variables we want to use\n",
      "    \n",
      "and returns the design matrix $\\mathbf X$ (and optionally also $y$).\n",
      "\n",
      "Formulae have the general form `y ~ x`.\n",
      "\n",
      "- everthing to the left of the `~` character are the things we want to predict (response variable)\n",
      "- everything to the right are the predictors\n",
      "- we can use the names of variables in our data frame to make the code more readable\n",
      "\n",
      "To make this more concrete, let's look at an example for our linear regression above."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# this command returns both X and y (hence \"dmatrices\" plural). See \"dmatrix\" if you just want X.\n",
      "y, X = patsy.dmatrices('TotalSleep ~ log_BodyWt', sleep)\n",
      "\n",
      "y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "DesignMatrix with shape (42, 1)\n",
        "  TotalSleep\n",
        "         8.3\n",
        "         3.9\n",
        "         9.8\n",
        "        19.7\n",
        "         6.2\n",
        "        14.5\n",
        "         9.7\n",
        "        12.5\n",
        "         3.9\n",
        "         8.4\n",
        "         8.6\n",
        "        10.7\n",
        "        10.7\n",
        "         3.8\n",
        "        14.4\n",
        "         6.2\n",
        "        13.8\n",
        "         8.2\n",
        "         2.9\n",
        "         9.1\n",
        "        19.9\n",
        "         8.0\n",
        "        13.2\n",
        "        12.8\n",
        "        19.4\n",
        "        17.4\n",
        "        17.0\n",
        "        10.9\n",
        "        13.7\n",
        "         8.4\n",
        "  [12 rows omitted]\n",
        "  Terms:\n",
        "    'TotalSleep' (column 0)\n",
        "  (to view full data, use np.asarray(this_obj))"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "`y` in this case is just the column vector of `TotalSleep`. What about `X`?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "DesignMatrix with shape (42, 2)\n",
        "  Intercept  log_BodyWt\n",
        "          1     0.00000\n",
        "          1     7.84267\n",
        "          1     2.35613\n",
        "          1    -3.77226\n",
        "          1     5.07517\n",
        "          1     1.19392\n",
        "          1     3.95432\n",
        "          1    -0.85567\n",
        "          1     6.14204\n",
        "          1    -2.59027\n",
        "          1     1.09861\n",
        "          1    -0.24207\n",
        "          1    -1.60944\n",
        "          1     3.31999\n",
        "          1    -2.12026\n",
        "          1     4.44265\n",
        "          1    -2.29263\n",
        "          1     0.03922\n",
        "          1     6.25575\n",
        "          1    -5.29832\n",
        "          1    -4.60517\n",
        "          1     4.12713\n",
        "          1    -3.77226\n",
        "          1    -3.03655\n",
        "          1     0.53063\n",
        "          1     1.25276\n",
        "          1    -0.73397\n",
        "          1     2.30259\n",
        "          1     0.48243\n",
        "          1     5.25750\n",
        "  [12 rows omitted]\n",
        "  Terms:\n",
        "    'Intercept' (column 0)\n",
        "    'log_BodyWt' (column 1)\n",
        "  (to view full data, use np.asarray(this_obj))"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note how the second column of `X` is just the log bodyweight values from our data frame. However, Patsy has added an additional column: the intercept, where each value is 1. What does this mean?\n",
      "\n",
      "When we do the regression, remember that we will estimate a $\\beta$ weight for each column, and that the value of the linear predictor for each row is $\\beta_1 x_1 + \\beta_2 x_2 + ... + \\beta_n x_n$. Thus, adding a column of ones to the design matrix means we are adding the value of $\\beta_1$ to each observation in our data set. This value is the *intercept term* ($c$) from our equation for a line, $y = mc + c$.\n",
      "\n",
      "So in our regression, our prediction for the total sleep of each observation will be\n",
      "\n",
      "$\\hat y = \\beta_1 + \\beta_2 \\mathrm{logBodyWt}$\n",
      "\n",
      "$\\beta_1$ and $\\beta_2$ are our model coefficents that will be estimated from the data. For now though, let's just think about them as two numbers that we're going to estimate by eye from the scatterplot above.\n",
      "\n",
      "When log bodyweight is zero, TotalSleep is about 12 hours. So let's set $\\beta_1 = 12$. Slope is a bit harder to estimate: I'm going to guess -4. Let's apply these weights to our design matrix to generate some predictions:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "betas = np.array([12., -4.])   # the . after the number makes it a floating-point number rather than an integer.\n",
      "yhat = np.inner(X, betas)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that taking the inner product (with the command `np.inner`) of a matrix and a row vector is the same as multiplying each column by its corresponding beta weight and then summing (i.e. $\\beta_1 x_1 + \\beta_2 x_2$).\n",
      "\n",
      "How similar are our predictions against the true values?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# this plot uses straight matplotlib commands, not seaborn:\n",
      "plt.scatter(yhat, y)\n",
      "plt.plot((-30, 40), (-30, 40), c=\".2\", ls=\"--\");\n",
      "plt.xlabel('yhat (predicted)')\n",
      "plt.ylabel('y (real)')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {
        "png": {
         "height": 273,
         "width": 392
        }
       },
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAxAAAAIjCAYAAACTYP1KAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkiRJUmP/B150zuPDMmV3AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10cc79da0>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "From the scatterplot (with dashed identity line) you can see that I got the slope reasonably wrong. Let's compute the errors:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "errors = y - yhat  # absolute errors for each data point\n",
      "squared_errors = errors ** 2  # squared errors\n",
      "sse = squared_errors.sum()  # sum of squared errors\n",
      "sse"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "array(303857.9545972171)"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Statsmodels\n",
      "\n",
      "Now we can use the Statsmodels package to estimate the best coefficients from the data. We will fit it using statsmodels' GLM function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fit = sm.GLM(y, X).fit() # fit the design matrices we specified above using Patsy...\n",
      "# let's look at the fit summary:\n",
      "print(fit.summary())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                 Generalized Linear Model Regression Results                  \n",
        "==============================================================================\n",
        "Dep. Variable:             TotalSleep   No. Observations:                   42\n",
        "Model:                            GLM   Df Residuals:                       40\n",
        "Model Family:                Gaussian   Df Model:                            1\n",
        "Link Function:               identity   Scale:                   14.0654402509\n",
        "Method:                          IRLS   Log-Likelihood:                -114.09\n",
        "Date:                Tue, 24 Feb 2015   Deviance:                       562.62\n",
        "Time:                        17:12:43   Pearson chi2:                     563.\n",
        "No. Iterations:                     4                                         \n",
        "==============================================================================\n",
        "                 coef    std err          z      P>|z|      [95.0% Conf. Int.]\n",
        "------------------------------------------------------------------------------\n",
        "Intercept     11.4046      0.599     19.049      0.000        10.231    12.578\n",
        "log_BodyWt    -0.9474      0.191     -4.965      0.000        -1.321    -0.573\n",
        "==============================================================================\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The above table shows the results of fitting the simple linear regression. There's a bunch of information here. Let's go through some of it.\n",
      "\n",
      "1. Note that we've fit a \"Gaussian\" model with the \"identity\" link function. That means we're doing ordinary linear regression, which as we said above is one case of the Generalised Linear Model. The identity link means that $f()$ (see above) is just the identity (i.e. it doesn't modify the linear predictor $\\mathbf X \\beta$ in any way).\n",
      "\n",
      "1. We had 42 observations (i.e. all the complete cases in our sleep set). The residual degrees of freedom equals the number of observations minus 2, because we estimated 2 parameters from the data (intercept and slope). \n",
      "\n",
      "1. The table at the bottom shows us information about the individual parameters we estimated. The coefficient value of the intercept is 11.4, which is pretty close to my guess of 12. The slope of log bodyweight is -0.95, so my slope estimate was pretty rubbish.\n",
      "\n",
      "1. The `z` score is the coefficient divided by its standard error, and the P value is testing whether that standardised coefficient score is different from zero. Both P values are highly significant here, so in this simple case we can infer that both parameters are contributing something useful to predicting the total amount of sleep. The final two columns give us the bounds of the confidence intervals on the coefficient estimates.\n",
      "\n",
      "Let's compare the predictions of this model to those of my guesses.\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "yhat_2 = fit.predict()\n",
      "\n",
      "# note that internally, the fit.predict() function does something similar \n",
      "# to our inner product between X and beta, above.\n",
      "\n",
      "plt.scatter(yhat_2, y)\n",
      "plt.plot((-30, 40), (-30, 40), c=\".2\", ls=\"--\");\n",
      "plt.xlabel('yhat_2 (predicted)')\n",
      "plt.ylabel('y (real)')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {
        "png": {
         "height": 273,
         "width": 392
        }
       },
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAxAAAAIjCAYAAACTYP1KAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10c96f7f0>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "errors = y - yhat_2  # absolute errors for each data point\n",
      "squared_errors = errors ** 2  # squared errors\n",
      "sse2 = squared_errors.sum()  # sum of squared errors\n",
      "sse2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "array(52753.18037853191)"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You can see that the fitted values (SSE = 52753) are far closer to the data than my guesses (SSE = 303857)... which is good."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Statsmodels formula inputs\n",
      "\n",
      "Note that we could also do the same thing by passing our Patsy formula to Statsmodels directly, using the statsmodels formula input:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "fit_2 = smf.glm(formula='TotalSleep ~ log_BodyWt', data=sleep).fit()\n",
      "print(fit_2.summary())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                 Generalized Linear Model Regression Results                  \n",
        "==============================================================================\n",
        "Dep. Variable:             TotalSleep   No. Observations:                   42\n",
        "Model:                            GLM   Df Residuals:                       40\n",
        "Model Family:                Gaussian   Df Model:                            1\n",
        "Link Function:               identity   Scale:                   14.0654402509\n",
        "Method:                          IRLS   Log-Likelihood:                -114.09\n",
        "Date:                Tue, 24 Feb 2015   Deviance:                       562.62\n",
        "Time:                        17:12:44   Pearson chi2:                     563.\n",
        "No. Iterations:                     4                                         \n",
        "==============================================================================\n",
        "                 coef    std err          z      P>|z|      [95.0% Conf. Int.]\n",
        "------------------------------------------------------------------------------\n",
        "Intercept     11.4046      0.599     19.049      0.000        10.231    12.578\n",
        "log_BodyWt    -0.9474      0.191     -4.965      0.000        -1.321    -0.573\n",
        "==============================================================================\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Graphically exploring model fit\n",
      "\n",
      "When fitting models, it's a good idea to look at graphical representations of model fit and the residuals (the distance between your predictions and your observations) to diagnose problems. Many plots of model fit are available in `Statsmodels`, at least for linear models (see [here](http://statsmodels.sourceforge.net/devel/examples/notebooks/generated/example_regression_plots.html)). \n",
      "\n",
      "We looked at one representation of the relationship between our model fits and the data above. Here are a few common plots."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# first we add to the sleep data frame, make a data frame of the stuff we want to plot:\n",
      "plots_df = sleep[['TotalSleep', 'log_BodyWt']].copy()\n",
      "plots_df['yhat'] = fit.predict()\n",
      "plots_df['resids'] = plots_df['TotalSleep'] - plots_df['yhat']  \n",
      "# note the fit object also contains various residuals.\n",
      "plots_df.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>TotalSleep</th>\n",
        "      <th>log_BodyWt</th>\n",
        "      <th>yhat</th>\n",
        "      <th>resids</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td>  8.3</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 11.404567</td>\n",
        "      <td>-3.104567</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td>  3.9</td>\n",
        "      <td> 7.842671</td>\n",
        "      <td>  3.974367</td>\n",
        "      <td>-0.074367</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5</th>\n",
        "      <td>  9.8</td>\n",
        "      <td> 2.356126</td>\n",
        "      <td>  9.172358</td>\n",
        "      <td> 0.627642</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>6</th>\n",
        "      <td> 19.7</td>\n",
        "      <td>-3.772261</td>\n",
        "      <td> 14.978433</td>\n",
        "      <td> 4.721567</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>7</th>\n",
        "      <td>  6.2</td>\n",
        "      <td> 5.075174</td>\n",
        "      <td>  6.596313</td>\n",
        "      <td>-0.396313</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "   TotalSleep  log_BodyWt       yhat    resids\n",
        "1         8.3    0.000000  11.404567 -3.104567\n",
        "4         3.9    7.842671   3.974367 -0.074367\n",
        "5         9.8    2.356126   9.172358  0.627642\n",
        "6        19.7   -3.772261  14.978433  4.721567\n",
        "7         6.2    5.075174   6.596313 -0.396313"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# plot predictions against real data:\n",
      "plt.scatter(sleep['log_BodyWt'], sleep['TotalSleep'], c='k')\n",
      "plt.plot(sleep['log_BodyWt'], fit.predict(), c='r')\n",
      "plt.xlabel('Log Bodyweight')\n",
      "plt.ylabel('Total Sleep')\n",
      "plt.legend(['Prediction', 'Data'])\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {
        "png": {
         "height": 273,
         "width": 386
        }
       },
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAwQAAAIjCAYAAAC9JdzYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEEiSJEk19v8BjtMDJ0e3kI4AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d1f1208>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Residual plots\n",
      "\n",
      "Looking at the residuals as a function of our predictors can show some problems with the modelling assumptions. Recall that our model expects the observations to be independent and the errors normally distributed. We can check this graphically with a few plots."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# plot residuals against bodyweight:\n",
      "resids = sleep['TotalSleep'] - fit.predict()\n",
      "plt.scatter(plots_df['log_BodyWt'], resids, c='k')\n",
      "plt.plot((-8, 10), (0, 0), 'r--')\n",
      "plt.xlabel('Log Bodyweight')\n",
      "plt.ylabel('Residuals')\n",
      "plt.tight_layout()\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {
        "png": {
         "height": 282,
         "width": 425
        }
       },
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAA1MAAAI1CAYAAAAzYqBvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10cf889b0>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Basically, we want the spread of the residuals around the zero line to look random. There shouldn't be anything systematic there -- if so, our model is missing non-random (i.e. predictable) relationships in the data.\n",
      "\n",
      "For example (from [here](http://www.r-bloggers.com/model-validation-interpreting-residual-plots/)):\n",
      "\n",
      "<img src=\"pics_for_lectures/resid-plots.gif\">\n",
      "\n",
      "If your residuals plots look something like (b)\u2013(f), think about expanding your model to capture the additional relationships in the data.\n",
      "\n",
      "The distribution of residuals should also be approximately normal:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.hist(resids.values);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {
        "png": {
         "height": 258,
         "width": 370
        }
       },
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAuUAAAIFCAYAAAB1foN8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10cf85320>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this case, it looks a little right-skewed. That is, we might be violating the assumption of normality in residuals, but probably not drastically."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Seaborn regression plots\n",
      "\n",
      "Handily, Seaborn allows you to do some of these plots directly, without even doing the statsmodels fitting first. This is great for quickly exploring relationships in data, and happily the plots are also much prettier than the default Matplotlib figures. [See here for examples and code](http://stanford.edu/~mwaskom/software/seaborn/tutorial/quantitative_linear_models.html#visualizing-multiple-regression-with-lmplot)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sns.lmplot('log_BodyWt', 'TotalSleep', data=sleep)\n",
      "sns.despine(offset=10, trim=True);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {
        "png": {
         "height": 364,
         "width": 363
        }
       },
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAtcAAALZCAYAAAB8hA0tAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d7069b0>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sns.residplot('log_BodyWt', 'TotalSleep', data=sleep)\n",
      "sns.despine(offset=10, trim=True);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {
        "png": {
         "height": 283,
         "width": 401
        }
       },
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAyMAAAI3CAYAAACI44T8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n4n+6X2VBI8XvmwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d7847b8>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Internally these functions are fitting the same regression model as we wrote out above, using statsmodels, and wrapping it into pretty exploratory plots for us."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Categorical variables and dummy coding\n",
      "\n",
      "Some variables of interest will be categorical rather than metric / continuous. For example:\n",
      "\n",
      "- gender is generally thought of as dichotomous (Male, Female)\n",
      "- a person's religion might be one of a number of categories (Christian, Muslim, Buddhist, nonbeliever, ...)\n",
      "- \"Species\" is an example from our dataset above\n",
      "\n",
      "**How are categorical variables handled in the design matrix?**\n",
      "\n",
      "Categorical variables are transformed into one or more design matrix columns with a specific meaning regarding the levels of the variable. The most common method, and the one we explore here, is called *Treatment* or *dummy coding*. You can see some examples of other coding schemes built into Patsy [here](http://patsy.readthedocs.org/en/latest/API-reference.html#categorical-coding-ref).\n",
      "\n",
      "For the purposes of this demonstration, let's create a categorical variable \"danger_cat\" where we consider animals with either *high* or *low* danger of predation / exposure."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sleep['danger_cat'] = 'low'  # set as a string, \"low\" for all.\n",
      "sleep.loc[sleep['Danger'] > 3, 'danger_cat'] = 'high'  # set Danger=4 or 5 to \"high\"\n",
      "sleep['danger_cat']"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "1      low\n",
        "4     high\n",
        "5     high\n",
        "6      low\n",
        "7     high\n",
        "8      low\n",
        "9      low\n",
        "10    high\n",
        "11    high\n",
        "14     low\n",
        "15     low\n",
        "16     low\n",
        "17     low\n",
        "21    high\n",
        "22     low\n",
        "24     low\n",
        "26     low\n",
        "27    high\n",
        "28    high\n",
        "31    high\n",
        "32     low\n",
        "33     low\n",
        "36     low\n",
        "37     low\n",
        "38     low\n",
        "39     low\n",
        "41     low\n",
        "42    high\n",
        "43     low\n",
        "44    high\n",
        "45    high\n",
        "47     low\n",
        "48     low\n",
        "49     low\n",
        "50     low\n",
        "51     low\n",
        "53    high\n",
        "56     low\n",
        "57     low\n",
        "58     low\n",
        "59    high\n",
        "60     low\n",
        "Name: danger_cat, dtype: object"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# how does total sleep appear to change according to our new categories?\n",
      "sns.set_context('notebook')\n",
      "g = sns.boxplot(sleep['TotalSleep'], groupby=sleep['danger_cat'])\n",
      "sns.despine(ax=g, offset=10);\n",
      "\n",
      "# Note how \"violinplot\" can be a bit misleading here, due to few cases and the kernel density smooth:\n",
      "# g = sns.violinplot(sleep['TotalSleep'], groupby=sleep['danger_cat'])\n",
      "# sns.despine(ax=g, offset=10);\n",
      "plt.savefig('blah.pdf')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {
        "png": {
         "height": 367,
         "width": 503
        }
       },
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAA+4AAALfCAYAAAD/tZgCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d74a198>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The low danger group seem to sleep for longer on average than the high danger group.\n",
      "\n",
      "Now imagine we want to use a GLM to test this impression. **Is the total amount of sleep in the high danger group less than the low danger group?**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y, X = patsy.dmatrices('TotalSleep ~ danger_cat', sleep)\n",
      "X"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "DesignMatrix with shape (42, 2)\n",
        "  Intercept  danger_cat[T.low]\n",
        "          1                  1\n",
        "          1                  0\n",
        "          1                  0\n",
        "          1                  1\n",
        "          1                  0\n",
        "          1                  1\n",
        "          1                  1\n",
        "          1                  0\n",
        "          1                  0\n",
        "          1                  1\n",
        "          1                  1\n",
        "          1                  1\n",
        "          1                  1\n",
        "          1                  0\n",
        "          1                  1\n",
        "          1                  1\n",
        "          1                  1\n",
        "          1                  0\n",
        "          1                  0\n",
        "          1                  0\n",
        "          1                  1\n",
        "          1                  1\n",
        "          1                  1\n",
        "          1                  1\n",
        "          1                  1\n",
        "          1                  1\n",
        "          1                  1\n",
        "          1                  0\n",
        "          1                  1\n",
        "          1                  0\n",
        "  [12 rows omitted]\n",
        "  Terms:\n",
        "    'Intercept' (column 0)\n",
        "    'danger_cat' (column 1)\n",
        "  (to view full data, use np.asarray(this_obj))"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now see that the design matrix column for `danger_cat` takes on two values: 0 (for high danger) and 1 (for low danger). What does this mean for the predictions? Let's think through what happens when we multiply these results by $\\beta$.\n",
      "\n",
      "When `danger_cat = 1`, \n",
      "\n",
      "$\\hat y = \\beta_1 * 1 + \\beta_2 * 1$\n",
      "\n",
      "when `danger_cat = 0`,\n",
      "\n",
      "$\\hat y = \\beta_1 * 1 + \\beta_2 * 0$\n",
      "\n",
      "That is, the intercept coefficient $\\beta_1$ represents the mean for the high danger group (`danger_cat = 0`), and the $\\beta_2$ coefficient represents the *difference* between the means of the high group and the low group.\n",
      "\n",
      "Let's see what those coefficients are:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fit = smf.glm(formula='TotalSleep ~ danger_cat', data=sleep).fit()\n",
      "print(fit.summary())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                 Generalized Linear Model Regression Results                  \n",
        "==============================================================================\n",
        "Dep. Variable:             TotalSleep   No. Observations:                   42\n",
        "Model:                            GLM   Df Residuals:                       40\n",
        "Model Family:                Gaussian   Df Model:                            1\n",
        "Link Function:               identity   Scale:                   16.8412589286\n",
        "Method:                          IRLS   Log-Likelihood:                -117.87\n",
        "Date:                Tue, 24 Feb 2015   Deviance:                       673.65\n",
        "Time:                        17:12:46   Pearson chi2:                     674.\n",
        "No. Iterations:                     4                                         \n",
        "=====================================================================================\n",
        "                        coef    std err          z      P>|z|      [95.0% Conf. Int.]\n",
        "-------------------------------------------------------------------------------------\n",
        "Intercept             7.2929      1.097      6.649      0.000         5.143     9.443\n",
        "danger_cat[T.low]     5.0250      1.343      3.741      0.000         2.392     7.658\n",
        "=====================================================================================\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The intercept coefficient is 7.29 hours of sleep. You can see from the box plot above that this corresponds to the mean of the high danger group. The difference between the high and low group (the coefficient for danger_cat) is 5.02 hours. That is, the mean of the low danger group is 7.29 + 5.02 = 12.31 hours (again, check that this looks right according to the box plot). \n",
      "\n",
      "We can see from the z scores that given the variance in the samples (std err), the intercept is significantly different to zero (i.e. the high danger group sleep significantly more than zero hours) and that the difference between the high and low danger groups is also significant (i.e. the low danger group sleeps for significantly longer than the high danger group).\n",
      "\n",
      "We've just tested two hypotheses. What do these tests remind you of?\n",
      "\n",
      "\n",
      "## t-tests\n",
      "\n",
      "Testing if the coefficient of the `danger_cat` variable is different to zero is (almost) the same as *an independent samples t-test*! It's not exactly the same because `glm` uses a z-test -- if we fitted the model with ordinary least squares [`smf.ols`] it would be exactly the same in this case.\n",
      "\n",
      "To prove to ourselves that these are equivalent, let's do the appropriate tests:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "high_array = sleep['TotalSleep'][sleep['danger_cat']=='high']\n",
      "low_array = sleep['TotalSleep'][sleep['danger_cat']=='low']"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# how does this compare to an independent groups z-test?\n",
      "t, p = sm_stats.weightstats.ztest(high_array, low_array)\n",
      "'Independent samples z-test: z = {t}, p = {p}'.format(t=np.round(t, decimals=3), p=p)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "'Independent samples z-test: z = -3.741, p = 0.00018341854744738338'"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "'Model values: z = {t}, p = {p}'.format(\n",
      "                        t=np.round(fit.tvalues[1], decimals=3), \n",
      "                        p=fit.pvalues[1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "'Model values: z = 3.741, p = 0.00018341854744738338'"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So we can see that the values from the model are exactly the same as a z-test. What about t?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fit_ols = smf.ols(formula='TotalSleep ~ danger_cat', data=sleep).fit()\n",
      "print(fit_ols.summary())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                            OLS Regression Results                            \n",
        "==============================================================================\n",
        "Dep. Variable:             TotalSleep   R-squared:                       0.259\n",
        "Model:                            OLS   Adj. R-squared:                  0.241\n",
        "Method:                 Least Squares   F-statistic:                     13.99\n",
        "Date:                Tue, 24 Feb 2015   Prob (F-statistic):           0.000575\n",
        "Time:                        17:12:46   Log-Likelihood:                -117.87\n",
        "No. Observations:                  42   AIC:                             239.7\n",
        "Df Residuals:                      40   BIC:                             243.2\n",
        "Df Model:                           1                                         \n",
        "Covariance Type:            nonrobust                                         \n",
        "=====================================================================================\n",
        "                        coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
        "-------------------------------------------------------------------------------------\n",
        "Intercept             7.2929      1.097      6.649      0.000         5.076     9.510\n",
        "danger_cat[T.low]     5.0250      1.343      3.741      0.001         2.310     7.740\n",
        "==============================================================================\n",
        "Omnibus:                        2.740   Durbin-Watson:                   1.526\n",
        "Prob(Omnibus):                  0.254   Jarque-Bera (JB):                1.557\n",
        "Skew:                           0.165   Prob(JB):                        0.459\n",
        "Kurtosis:                       2.117   Cond. No.                         3.23\n",
        "==============================================================================\n",
        "\n",
        "Warnings:\n",
        "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t, p, df = sm_stats.weightstats.ttest_ind(low_array, high_array)\n",
      "'Independent samples t-test: t({df}) = {t}, p = {p}'.format(\n",
      "    t=np.round(t, decimals=3), df=int(df), p=p)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "'Independent samples t-test: t(40) = 3.741, p = 0.0005752964234035196'"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "'Model values: t = {t}, p = {p}'.format(\n",
      "                        t=np.round(fit_ols.tvalues[1], decimals=3), \n",
      "                        p=fit_ols.pvalues[1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "'Model values: t = 3.741, p = 0.0005752964234035218'"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "They are identical to high precision!"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## One-sample test (mean of `high` different to zero)\n",
      "\n",
      "The test of the regression coefficient for the intercept is conceptually the same as a one-sample t-test: we ask whether the mean of the \"high\" group is different to zero. In practice however, because the standard errors in the regression are calculated using the entire design matrix, the test statistics and confidence intervals for the intercept are not the same as a one-sample t-test. Loosely, the standard errors of the intercept depend on the total variance in the dataset (i.e. all variables included in the regression), whereas in the separate one-sample test they do not."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# using statsmodels, must first compute \"descrstats\":\n",
      "d1 = sm_stats.weightstats.DescrStatsW(high_array)\n",
      "t, p = d1.ztest_mean(0)\n",
      "'Independent z-test: z = {t}, p = {p}'.format(\n",
      "    t=np.round(t, decimals=3), p=p)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "'Independent z-test: z = 8.632, p = 6.026877856701133e-18'"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Is this the same as from the linear model fit?\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "'Model values: z = {t}, p = {p}'.format(\n",
      "                        t=np.round(fit.tvalues[0], decimals=3), \n",
      "                        p=fit.pvalues[0])\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "'Model values: z = 6.649, p = 2.9453554513479515e-11'"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So we can see that the test statistics for the intercept are not the same: 8.632 in the separate test compared to 6.64 in the regression model. As mentioned above, the total variance in the design matrix contributes to the standard errors. \n",
      "\n",
      "We can check that it's equivalent to fitting an intercept-only model to just the `high` dataset:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# cell to check \"high\" alone\n",
      "high_only = sleep.copy()\n",
      "high_only = high_only[high_only['danger_cat']=='high']\n",
      "fit_high = smf.glm(formula='TotalSleep ~ 1', data=high_only).fit()\n",
      "print(fit_high.summary())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                 Generalized Linear Model Regression Results                  \n",
        "==============================================================================\n",
        "Dep. Variable:             TotalSleep   No. Observations:                   14\n",
        "Model:                            GLM   Df Residuals:                       13\n",
        "Model Family:                Gaussian   Df Model:                            0\n",
        "Link Function:               identity   Scale:                   9.99302197802\n",
        "Method:                          IRLS   Log-Likelihood:                -35.460\n",
        "Date:                Tue, 24 Feb 2015   Deviance:                       129.91\n",
        "Time:                        17:12:46   Pearson chi2:                     130.\n",
        "No. Iterations:                     4                                         \n",
        "==============================================================================\n",
        "                 coef    std err          z      P>|z|      [95.0% Conf. Int.]\n",
        "------------------------------------------------------------------------------\n",
        "Intercept      7.2929      0.845      8.632      0.000         5.637     8.949\n",
        "==============================================================================\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So in this case, where the `low` cases are excluded and we only fit an intercept, the GLM is the same as the separate one-sample test."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Categorical variable with more than one level\n",
      "\n",
      "We learned above that \"dummy coding\" is when you transform a categorical variable into 0s and 1s in the design matrix. How does this work for categorical variables with more than two levels?\n",
      "\n",
      "Let's try by treating the \"Lifespan\" variable (continuous, lifespan in years) as a *categorical* rather than *continuous* variable. I will create a new variable, grouping lifespan into three categories: short, medium, long.\n",
      "\n",
      "To do this we will use Pandas' `qcut` function, which cuts a variable into groups based on quantiles. This creates a new Pandas Series whose type is `categorical`. While categories are going to be really useful in the future, right now they don't play nice with other packages (like statsmodels). For this reason, we will convert the category data type to a plain old object. See the docs for categories [here](https://pandas-docs.github.io/pandas-docs-travis/categorical.html)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sleep['life_cat'] = pd.qcut(sleep['LifeSpan'], [0, .33, .66, 1])\n",
      "sleep['life_cat']\n",
      "\n",
      "# category labels are a bit ugly, reflecting range of cuts:"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "1          [2, 6.765]\n",
        "4       (20.428, 100]\n",
        "5       (20.428, 100]\n",
        "6     (6.765, 20.428]\n",
        "7       (20.428, 100]\n",
        "8       (20.428, 100]\n",
        "9       (20.428, 100]\n",
        "10    (6.765, 20.428]\n",
        "11      (20.428, 100]\n",
        "14         [2, 6.765]\n",
        "15      (20.428, 100]\n",
        "16         [2, 6.765]\n",
        "17    (6.765, 20.428]\n",
        "21    (6.765, 20.428]\n",
        "22         [2, 6.765]\n",
        "24      (20.428, 100]\n",
        "26    (6.765, 20.428]\n",
        "27    (6.765, 20.428]\n",
        "28      (20.428, 100]\n",
        "31         [2, 6.765]\n",
        "32      (20.428, 100]\n",
        "33      (20.428, 100]\n",
        "36         [2, 6.765]\n",
        "37         [2, 6.765]\n",
        "38         [2, 6.765]\n",
        "39         [2, 6.765]\n",
        "41    (6.765, 20.428]\n",
        "42    (6.765, 20.428]\n",
        "43    (6.765, 20.428]\n",
        "44      (20.428, 100]\n",
        "45    (6.765, 20.428]\n",
        "47         [2, 6.765]\n",
        "48    (6.765, 20.428]\n",
        "49      (20.428, 100]\n",
        "50    (6.765, 20.428]\n",
        "51         [2, 6.765]\n",
        "53    (6.765, 20.428]\n",
        "56         [2, 6.765]\n",
        "57    (6.765, 20.428]\n",
        "58         [2, 6.765]\n",
        "59      (20.428, 100]\n",
        "60         [2, 6.765]\n",
        "Name: life_cat, dtype: category\n",
        "Categories (3, object): [[2, 6.765] < (6.765, 20.428] < (20.428, 100]]"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# change category labels, then convert to object:\n",
      "sleep['life_cat'] = sleep['life_cat'].cat.rename_categories(['short', 'med', 'long']) # rename categories\n",
      "sleep['life_cat'] = sleep['life_cat'].astype('object')  # make it an object, rather than a category\n",
      "sleep['life_cat']"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "1     short\n",
        "4      long\n",
        "5      long\n",
        "6       med\n",
        "7      long\n",
        "8      long\n",
        "9      long\n",
        "10      med\n",
        "11     long\n",
        "14    short\n",
        "15     long\n",
        "16    short\n",
        "17      med\n",
        "21      med\n",
        "22    short\n",
        "24     long\n",
        "26      med\n",
        "27      med\n",
        "28     long\n",
        "31    short\n",
        "32     long\n",
        "33     long\n",
        "36    short\n",
        "37    short\n",
        "38    short\n",
        "39    short\n",
        "41      med\n",
        "42      med\n",
        "43      med\n",
        "44     long\n",
        "45      med\n",
        "47    short\n",
        "48      med\n",
        "49     long\n",
        "50      med\n",
        "51    short\n",
        "53      med\n",
        "56    short\n",
        "57      med\n",
        "58    short\n",
        "59     long\n",
        "60    short\n",
        "Name: life_cat, dtype: object"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So now we have a new categorical variable, `life_cat`, with three levels. In this case it would be appropriate to analyse the categories as ordered (see [here](http://patsy.readthedocs.org/en/latest/API-reference.html#categorical-coding-ref) for how to do that in Patsy, and [here](http://www.ats.ucla.edu/stat/sas/webbooks/reg/chapter5/sasreg5.htm) for a discussion of different coding schemes). However, for simplicity here we're going to treat this as *unordered*, meaning that our model thinks the category order doesn't matter (e.g. with something like religion). \n",
      "\n",
      "What does Patsy do when we make a design matrix using a categorical predictor with more than 2 levels?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y, X = patsy.dmatrices('TotalSleep ~ life_cat', sleep)\n",
      "X"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "DesignMatrix with shape (42, 3)\n",
        "  Intercept  life_cat[T.med]  life_cat[T.short]\n",
        "          1                0                  1\n",
        "          1                0                  0\n",
        "          1                0                  0\n",
        "          1                1                  0\n",
        "          1                0                  0\n",
        "          1                0                  0\n",
        "          1                0                  0\n",
        "          1                1                  0\n",
        "          1                0                  0\n",
        "          1                0                  1\n",
        "          1                0                  0\n",
        "          1                0                  1\n",
        "          1                1                  0\n",
        "          1                1                  0\n",
        "          1                0                  1\n",
        "          1                0                  0\n",
        "          1                1                  0\n",
        "          1                1                  0\n",
        "          1                0                  0\n",
        "          1                0                  1\n",
        "          1                0                  0\n",
        "          1                0                  0\n",
        "          1                0                  1\n",
        "          1                0                  1\n",
        "          1                0                  1\n",
        "          1                0                  1\n",
        "          1                1                  0\n",
        "          1                1                  0\n",
        "          1                1                  0\n",
        "          1                0                  0\n",
        "  [12 rows omitted]\n",
        "  Terms:\n",
        "    'Intercept' (column 0)\n",
        "    'life_cat' (columns 1:3)\n",
        "  (to view full data, use np.asarray(this_obj))"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You can see that we now have the intercept plus *two* additional columns, whose values can be zero or one. Take a look down the columns and compare them to the values of `sleep['life_cat']` above. \n",
      "\n",
      "Let's take for example the first 5 rows:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sleep['life_cat'].head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "1    short\n",
        "4     long\n",
        "5     long\n",
        "6      med\n",
        "7     long\n",
        "Name: life_cat, dtype: object"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X[0:5, :]  # first five rows, and second two cols of X"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 36,
       "text": [
        "array([[ 1.,  0.,  1.],\n",
        "       [ 1.,  0.,  0.],\n",
        "       [ 1.,  0.,  0.],\n",
        "       [ 1.,  1.,  0.],\n",
        "       [ 1.,  0.,  0.]])"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's work through what this means for the Beta weights:\n",
      "\n",
      "**For rows where 'life_cat' is 'long'**, the value of the two X columns is `[0, 0]`. Therefore, the prediction for TotalSleep in these rows is:\n",
      "\n",
      "$\\hat y = \\beta_1 * 1 + \\beta_2 * 0 + \\beta_3 * 0$\n",
      "\n",
      "$\\hat y = \\beta_1$\n",
      "\n",
      "The first beta weight (the intercept) is therefore the mean of the 'long' group.\n",
      "\n",
      "**For rows where 'life_cat' is 'short'**, the value of the two X columns is `[1, 0]`. Therefore, the prediction for TotalSleep in these rows is:\n",
      "\n",
      "$\\hat y = \\beta_1 * 1 + \\beta_2 * 1 + \\beta_3 * 0$\n",
      "\n",
      "$\\hat y = \\beta_1 + \\beta_2$\n",
      "\n",
      "The second beta weight is therefore the average *difference* between the 'long' group and the 'short' group.\n",
      "\n",
      "Finally, **for rows where 'life_cat' is 'med'**, the value of the two X columns is `[0, 1]`. Therefore, the prediction for TotalSleep in these rows is:\n",
      "\n",
      "$\\hat y = \\beta_1 * 1 + \\beta_2 * 0 + \\beta_3 * 1$\n",
      "\n",
      "$\\hat y = \\beta_1 + \\beta_3$\n",
      "\n",
      "The third beta weight is therefore the average *difference* between the 'long' group and the 'med' group.\n",
      "\n",
      "Let's see what these coefficients turn out to be, by fitting the model:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fit = smf.glm('TotalSleep ~ life_cat', sleep).fit()\n",
      "print(fit.summary())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                 Generalized Linear Model Regression Results                  \n",
        "==============================================================================\n",
        "Dep. Variable:             TotalSleep   No. Observations:                   42\n",
        "Model:                            GLM   Df Residuals:                       39\n",
        "Model Family:                Gaussian   Df Model:                            2\n",
        "Link Function:               identity   Scale:                   20.0783516484\n",
        "Method:                          IRLS   Log-Likelihood:                -121.03\n",
        "Date:                Tue, 24 Feb 2015   Deviance:                       783.06\n",
        "Time:                        17:12:46   Pearson chi2:                     783.\n",
        "No. Iterations:                     4                                         \n",
        "=====================================================================================\n",
        "                        coef    std err          z      P>|z|      [95.0% Conf. Int.]\n",
        "-------------------------------------------------------------------------------------\n",
        "Intercept             8.7071      1.198      7.271      0.000         6.360    11.054\n",
        "life_cat[T.med]       1.6000      1.694      0.945      0.345        -1.719     4.919\n",
        "life_cat[T.short]     4.2071      1.694      2.484      0.013         0.888     7.527\n",
        "=====================================================================================\n"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If we add up these coefficients, we get some predictions for the mean amount of sleep in each category (intercept is just for the 'long' group):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "long_mean = fit.params[0]\n",
      "short_mean = fit.params[0] + fit.params[2]\n",
      "med_mean = fit.params[0] + fit.params[1]\n",
      "\n",
      "print('the predictions are: \\\n",
      "      \\n long = {} \\\n",
      "      \\n med = {} \\\n",
      "      \\n short = {}'.format(np.round(long_mean, decimals=1), \n",
      "                          np.round(med_mean, decimals=1), \n",
      "                          np.round(short_mean, decimals=1)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the predictions are:       \n",
        " long = 8.7       \n",
        " med = 10.3       \n",
        " short = 12.9\n"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's check that against a boxplot (which plots medians, but will give us a good idea):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "g = sns.boxplot(sleep['TotalSleep'], groupby=sleep['life_cat'])\n",
      "sns.despine(ax=g, offset=10);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {
        "png": {
         "height": 367,
         "width": 503
        }
       },
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAA+4AAALfCAYAAAD/tZgCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSZIkSTX2/3b2rF74txJ7AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10ec42978>"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So that looks about right. As before, the z-tests of the coefficients compare groups. The 'short' lifespan group gets significantly more hours of sleep than the 'long' lifespan group (P = .013), but the difference between the 'med' and 'long' groups is not significant (P = .345)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Reference level\n",
      "\n",
      "In the scheme of setting up design matrices we use here, a categorical predictor will have $k - 1$ columns in the design matrix, where $k$ is the number of categories. For example, in our two category (Danger = low or high) example from before, there was $2 - 1 = 1$ column of the design matrix for this categorical predictor.\n",
      "\n",
      "Note how the intercept takes on a meaning in these designs: the prediction for one of the categories. The category that corresponds to the intercept (or, when all the columns for this variable are zero) is called the *reference level* or *reference category*. The additional design matrix columns tell us how the non-reference categories differ from the reference level.\n",
      "\n",
      "In Patsy, we can specify the reference level manually (e.g. if we wanted the intercept to be the mean of the 'short' group rather than the 'long' group). See the Patsy documentation [here](http://patsy.readthedocs.org/en/latest/categorical-coding.html) for how to do this."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Your homework: multiple predictors\n",
      "\n",
      "In each example above, we have fit GLMs with single predictor variables. It is possible to expand our design matrix to include multiple predictors. In Patsy, the `+` operator is used to add a predictor to the design matrix. \n",
      "\n",
      "In a new notebook file, you should\n",
      "\n",
      "1. Import the sleep data\n",
      "1. Create the new variables (log_BodyWt, danger_cat, life_cat) by copying the code from this notebook.\n",
      "1. Fit the model \"`TotalSleep ~ log_BodyWt + danger_cat + life_cat`\"\n",
      "1. Think about the meaning of the coefficients. Write down what each coefficient means.\n",
      "1. Bonus: work out the predicted total sleep for a species that is\n",
      "    - low danger\n",
      "    - medium lifespan\n",
      "    - weighs 13 kg."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.core.display import HTML\n",
      "\n",
      "def css_styling():\n",
      "    styles = open(\"../custom_style.css\", \"r\").read()\n",
      "    return HTML(styles)\n",
      "css_styling()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<style>\n",
        "    @font-face {\n",
        "        font-family: \"Computer Modern\";\n",
        "        src: url('http://9dbb143991406a7c655e-aa5fcb0a5a4ec34cff238a2d56ca4144.r56.cf5.rackcdn.com/cmunss.otf');\n",
        "    }\n",
        "    @font-face {\n",
        "        font-family: \"Computer Modern\";\n",
        "        font-weight: bold;\n",
        "        src: url('http://9dbb143991406a7c655e-aa5fcb0a5a4ec34cff238a2d56ca4144.r56.cf5.rackcdn.com/cmunsx.otf');\n",
        "    }\n",
        "    @font-face {\n",
        "        font-family: \"Computer Modern\";\n",
        "        font-style: oblique;\n",
        "        src: url('http://9dbb143991406a7c655e-aa5fcb0a5a4ec34cff238a2d56ca4144.r56.cf5.rackcdn.com/cmunsi.otf');\n",
        "    }\n",
        "    @font-face {\n",
        "        font-family: \"Computer Modern\";\n",
        "        font-weight: bold;\n",
        "        font-style: oblique;\n",
        "        src: url('http://9dbb143991406a7c655e-aa5fcb0a5a4ec34cff238a2d56ca4144.r56.cf5.rackcdn.com/cmunso.otf');\n",
        "    }\n",
        "    div.cell{\n",
        "        width:850px;\n",
        "        font-size: 11pt;\n",
        "        margin-left:16% !important;\n",
        "        margin-right:auto;\n",
        "    }\n",
        "    h1 {\n",
        "        font-family: Minion Pro, serif;\n",
        "    }\n",
        "    h2 {\n",
        "        font-family: Minion Pro, serif;\n",
        "    }\n",
        "    h3 {\n",
        "        font-family: Minion Pro, serif;\n",
        "    }\n",
        "    h4{\n",
        "        margin-top:12px;\n",
        "        margin-bottom: 3px;\n",
        "       }\n",
        "    div.text_cell_render{\n",
        "        font-family: Optima, sans-serif;\n",
        "        line-height: 145%;\n",
        "        font-size: 12pt;\n",
        "        width:850px;\n",
        "        margin-left:auto;\n",
        "        margin-right:auto;\n",
        "    }\n",
        "    .CodeMirror{\n",
        "            font-family: \"Source Code Pro\", source-code-pro,Consolas, monospace;\n",
        "    }\n",
        "    .prompt{\n",
        "        display: None;\n",
        "    }\n",
        "    .text_cell_render h5 {\n",
        "        font-weight: 300;\n",
        "        font-size: 12pt;\n",
        "        color: #4057A1;\n",
        "        font-style: italic;\n",
        "        margin-bottom: .5em;\n",
        "        margin-top: 0.5em;\n",
        "        display: block;\n",
        "    }\n",
        "\n",
        "    .warning{\n",
        "        color: rgb( 240, 20, 20 )\n",
        "        }\n",
        "</style>\n",
        "<script>\n",
        "    MathJax.Hub.Config({\n",
        "                        TeX: {\n",
        "                           extensions: [\"AMSmath.js\"]\n",
        "                           },\n",
        "                tex2jax: {\n",
        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
        "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
        "                },\n",
        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
        "                \"HTML-CSS\": {\n",
        "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
        "                }\n",
        "        });\n",
        "</script>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "<IPython.core.display.HTML at 0x105e31940>"
       ]
      }
     ],
     "prompt_number": 1
    }
   ],
   "metadata": {}
  }
 ]
}